Resources · Managerial Economics
Break-even analysis: contribution, P/V ratio and margin of safety
The break-even formulas, worked through one example drawn to scale: contribution, P/V ratio, break-even point, target profit and margin of safety.
What break-even analysis answers
Break-even analysis, part of cost-volume-profit (CVP) analysis, tells a manager how many units must be sold to cover all costs, how profit changes with volume, and how much sales can fall before the business makes a loss. It rests on one split: fixed costs (rent, salaries, insurance), which stay the same whatever the output, and variable costs (materials, direct labour, packing), which rise with every unit made.
The formulas
| Measure | Formula |
|---|---|
| Contribution per unit | Selling price − Variable cost per unit |
| Total contribution | Sales − Total variable cost = Fixed cost + Profit |
| P/V ratio | Contribution ÷ Sales × 100 |
| Break-even point (units) | Fixed cost ÷ Contribution per unit |
| Break-even sales (₹) | Fixed cost ÷ P/V ratio |
| Sales for a target profit (units) | (Fixed cost + Target profit) ÷ Contribution per unit |
| Margin of safety | Actual sales − Break-even sales |
| Margin of safety ratio | Margin of safety ÷ Actual sales × 100 |
| Profit | Margin of safety × P/V ratio |
Worked example
A small unit in Tiruchirappalli makes school bags.
- Selling price: ₹500 a bag
- Variable cost: ₹300 a bag
- Fixed cost: ₹2,00,000 a month
- Actual sales this month: 1,500 bags
1. Contribution per unit = 500 − 300 = ₹200. Every bag sold adds ₹200 towards fixed cost, and once fixed cost is covered, ₹200 to profit.
2. P/V ratio = 200 ÷ 500 × 100 = 40%.
3. Break-even point = 2,00,000 ÷ 200 = 1,000 bags. In rupees: 2,00,000 ÷ 40% = ₹5,00,000 (check: 1,000 × ₹500).
4. Sales needed for a profit of ₹60,000 = (2,00,000 + 60,000) ÷ 200 = 1,300 bags, or ₹6,50,000.
5. Profit at actual sales of 1,500 bags = 1,500 × 200 − 2,00,000 = ₹1,00,000.
6. Margin of safety = 1,500 − 1,000 = 500 bags, or ₹7,50,000 − ₹5,00,000 = ₹2,50,000. As a ratio: 2,50,000 ÷ 7,50,000 = 33.3%. Sales can fall by a third before the unit makes a loss.
Check: profit = margin of safety × P/V ratio = 2,50,000 × 40% = ₹1,00,000. ✓
Reading the break-even chart
The figure above is drawn to scale from these numbers.
- The fixed cost line is flat at ₹2 lakh.
- The total cost line starts at ₹2 lakh (the fixed cost) and rises by ₹300 for every bag.
- The sales revenue line starts at zero and rises by ₹500 for every bag.
- Where revenue crosses total cost is the break-even point. To the left is the loss area, to the right the profit area.
- The horizontal gap between actual sales and the break-even point is the margin of safety.
What changes the break-even point
| Change | Effect on break-even point |
|---|---|
| Fixed cost rises | Rises |
| Selling price rises | Falls (contribution per unit rises) |
| Variable cost per unit rises | Rises (contribution per unit falls) |
| Sales volume rises | No change; margin of safety rises |
Try it with the example: if rent goes up so that fixed cost becomes ₹2,40,000, break-even rises to 1,200 bags. If the price rises to ₹550, contribution becomes ₹250 and break-even falls to 800 bags.
Uses and limitations
Uses: setting sales targets, pricing decisions, deciding whether to make or buy, judging the risk of a new product or branch, and planning how far costs must fall to survive a slump.
Limitations: costs are rarely perfectly fixed or perfectly variable; selling prices often fall with volume (discounts); a multi-product firm’s break-even depends on its sales mix; and the analysis is static, a picture of one period.
Practice questions
- Explain break-even analysis and its assumptions. Draw a break-even chart.
- Fixed cost ₹1,50,000; selling price ₹60 a unit; variable cost ₹35 a unit. Find the P/V ratio, break-even point in units and rupees, and the sales needed for a profit of ₹50,000. (Answer: 41.67%; 6,000 units, ₹3,60,000; 8,000 units.)
- Sales ₹4,00,000, profit ₹40,000, P/V ratio 25%. Find the fixed cost, break-even sales and margin of safety. (Answer: ₹60,000; ₹2,40,000; ₹1,60,000.)
- What is the margin of safety? How can a firm improve it?
Questions students ask
What is the break-even point?
The break-even point is the level of output or sales at which total revenue equals total cost, so the firm makes neither a profit nor a loss. In units it is fixed cost divided by contribution per unit; in rupees it is fixed cost divided by the P/V ratio.
What is the P/V ratio?
The profit-volume (P/V) ratio is contribution as a percentage of sales: (selling price − variable cost) ÷ selling price × 100. It shows how much of every rupee of sales is left to cover fixed costs and then add to profit. It can also be found as change in profit ÷ change in sales.
What is the margin of safety?
The margin of safety is the amount by which actual (or budgeted) sales exceed break-even sales. It shows how far sales can fall before the firm starts making a loss. Margin of safety = actual sales − break-even sales, or profit ÷ P/V ratio.
What are the assumptions of break-even analysis?
Costs can be split cleanly into fixed and variable; fixed costs stay constant over the relevant range; variable cost per unit and selling price stay constant; output produced equals output sold; and, for a multi-product firm, the sales mix stays the same.
What is the angle of incidence?
The angle of incidence is the angle at which the sales line cuts the total cost line on a break-even chart. A large angle means profits grow quickly once the firm passes break-even, which indicates a high P/V ratio.